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Abstract

We report the first experimental realization of an all-optical temporal integrator. The integrator is implemented using an all-fiber active (gain-assisted) filter based on superimposed fiber Bragg gratings made in an Er-Yb co-doped optical fiber that behaves like an ‘optical capacitor’. Functionality of this device was tested by integrating different optical pulses, with time duration down to 60 ps, and by integration of two consecutive pulses that had different relative phases, separated by up to 1 ns. The potential of the developed device for implementing all-optical computing systems for solving ordinary differential equations was also experimentally tested.

Fig. 3. Experimental results demonstrating time-domain integration of a single optical Gaussian pulse for two different input pulse FWHM time widths ((a) 140 ps and (b) 60 ps). The temporal optical intensity of the input pulse (orange curve) and the integrator output (green curve) are captured using a 20-GHz photoreceiver. For comparison, the square of the numerically calculated time cumulative integral of the measured input pulse field (square root of the measured temporal intensity profile) is also shown (yellow curve).

Fig. 4. (a) Diagram showing all-optical integration of two consecutive optical pulses with different relative phases. For relative phases of 0 (in-phase – the field amplitudes are of the same sign, red curves) and π (out-of-phase – the field amplitudes are of opposite signs, blue curves), the time integral is expected to be a double step-rising waveform, and a flat-top waveform, respectively. (b) Experimental setup for the double pulse integration. 14-ps pulses are generated from the FFL followed by an optical bandpass filter (0.4 nm 3dB-bandwidth). Time-delayed pulse replicas are made by using a fiber-coupled Michelson interferometer. For the shortest time delay (170 ps), we confirmed the relative phase of the two pulses measuring the optical spectrum of the double-pulse structure, which is shown in the inset: for in-phase pulses (red line), the spectrum has a maximum at the integrator central frequency, while for the out-of-phase pulses (blue line), there is a minimum. The output spectrum is shown as green line.

Fig. 7. (a) Schematic diagram of an integrator-based optical computing system designed for solving the first-order linear ordinary differential equation (ODE) defined in the figure. The two graphs at the bottom show the experimental (solid curves) and numerical (circles) solutions of the ODE for two different input optical signals: (b) an input ultrashort temporal impulse (FWHM time-width=60 ps) and (c) a constant excitation over a limited temporal window (2.9-ns long square-like pulse). In each case, the ODE is solved for different positive values of the parameter k.